Since non-woven fabrics produced by using heat-melt-adhesive fibers do not contain a chemical binder such as an adhesive, the fabrics are excellent in safety, and thus they have widely been used. Since polyolefin type non-woven fabrics are excellent in performances and economy in particular, they have been used in many fields such as operating gowns, medical supplies such as paper diapers and sanitary napkins, civil engineering materials, farming materials, and industrial materials. Method for producing heat-melt-adhesion type non-woven fabrics are broadly divided into a through-air method using heated air and a heated-roll method. Whereas the through-air method can be applied to polyethylene/polypropylene composite fibers, it has a problem that productivity is low since processing speed is slow compared with the heated-roll method. On the other hand, the heated-roll method has an advantage of being excellent in the productivity since the processing speed is high. As fibers suitable for the heated-roll method, polypropylene fibers comprising an ethylene-propylene random copolymer having a softening point of lower than 132.degree. C. and containing a prescribed amount of ethylene unit are proposed in Laid-open Japanese Patent Publication No. Sho 62-156310. However, the fibers have such defects that the hand feeling of non-woven fabrics produced by using the fibers is poor and that the range of fiber processing temperature at which non-woven fabrics having a strength sufficient to stand practical uses can be produced is extremely narrow. Non-woven fabrics comprising polypropylene fibers of a low stereo-regularity having a specific isotactic pentad fraction are proposed in Laid-open Japanese Patent Publication No. Hei 2-112456. Whereas the non-woven fabrics have a good hand feeling, their strength is not satisfactory. Whereas polypropylene fibers having a specific compound blended therein are proposed in Laid-open Japanese Patent Publication No. Hei 2-264012, the fibers are not sufficient either in hand feeling and in strength. A method for producing non-woven fabrics in which fibers are strongly heat-melt-adhered, and thus having a high strength, by using fibers which have three domains (i.e., surface domain, intermediate domain, and inner domain) in which molecular weight of the polymer successively increases from the surface portion toward the core portion, formed by oxidative-deterioration from the surface portion toward the core portion of the fiber is disclosed in Laid-open Japanese Patent Publication No. Hei 4-228666. Further, a fact that non-woven fabrics in which filaments or short fibers are strongly heat-melt-adhered can be obtained by using filaments or short fibers having a skin-core structure is disclosed in Laid-open Japanese Patent Publication No. Hei 7-11508. However, these non-woven fabrics can not be said to be satisfactory from the viewpoint of the balance of the strength with the hand feeling of non-woven fabrics.